Dealing with numerical noise in CFD-based design optimization

Abstract

SUMMARYNumerical noise is an inevitable by-product of Computational Fluid Dynamics (CFD) simulations which can lead to challenges in finding optimum designs. This article draws attention to the issue, illustrating the difficulties it can cause for road vehicle aerodynamics simulations. Firstly a benchmark problem is used to assess a range of turbulence models and grid types. Large noise amplitudes up to 22% are evident for solutions computed on unstructured tetrahedral grids whereas computations on hexahedral and polyhedral grid structures exhibit substantially less noise. The Spalart Allmaras turbulence model is shown to be far less susceptible to noise levels than two other commonly-used models for this application.Secondly, multi-objective aerodynamic shape optimization is applied to a fairing for a practical road vehicle which is parameterised in terms of three design variables. Moving Least Squares (MLS) metamodels are constructed from 50 highfidelity CFD solutions for two objective functions. Subsequent optimization is successful for the first objective, however numerical noise levels in excess of 7% give rise to difficulties for the second one. A revision to the problem leads to success and the construction of a small Pareto Front. Further analysis underlines the inherent capability of MLS metamodels in dealing with noisy CFD responses.

Aerodynamic Drag Reduction of Emergency Response Vehicles

“…Table 2 shows that the CFD predictions of C D on the two finest grids are effectively grid-independent and that the realizable k-ε model agrees reasonably well with experiment while the standard one is in much more poorer agreement. This is consistent with the findings of Gilkeson et al [23] for similarly bluff vehicles ( Table 2). …”

“…Metamodels (also often termed response surfaces) for D were then built using the Moving Least Squares (MLS) method [27,28] within Altair Hyperstudy [29]. This technique can cater for the noisy responses that can be encountered in vehicle aerodynamics [23]. The metamodel can be tuned by selecting an appropriate 'closeness of fit parameter', θ, which is contained within a Gaussian weight decay function, namely 2 …”

A Numerical Investigation of Through-Tool Coolant Wetting Behaviour in Twist-Drilling

“…where ‖ − ‖ = ( − ) 2 + ( − ) 2 is the Euclidean distance between the design point = ( , ) at which the MLS metamodel is being evaluated, and the ith DoE point ( , ), and is the closeness of fit parameter. A large value of ensures the MLS metamodel reproduces the known DoE point values accurately, whereas a smaller value of can reduce the effect of numerical noise on the metamodel [23]. The values of for the metamodel are selected by minimising the Root Mean Square Error (RMSE) between the predictions from the metamodel and those from the CFD at the DoE points.…”

A Numerical Investigation of Through-Tool Coolant Wetting Behaviour in Twist-Drilling

“…A large value of β ensures the MLS metamodel reproduces the known DoE point values accurately, whereas a smaller value of β can reproduce the effect of numerical noise on the metamodel [22]. The vales of β for the metamodel are selected by minimising the Root Mean Square Error (RMSE) between the predictions from the metamodel and those from the CFD at the DoE points.…”